   COORDINATIONNUMBER
 This is part of the multicolvar module

Calculate the coordination numbers of atoms so that you can then calculate functions of the distribution of coordination numbers such as the minimum, the number less than a certain quantity and so on.

So that the calculated coordination numbers have continuous derivatives the following function is used:

$s = \frac{ 1 - \left(\frac{r-d_0}{r_0}\right)^n } { 1 - \left(\frac{r-d_0}{r_0}\right)^m }$

If R_POWER is set, this will use the product of pairwise distance raised to the R_POWER with the coordination number function defined above. This was used in White and Voth  as a way of indirectly biasing radial distribution functions. Note that in that reference this function is referred to as moments of coordination number, but here we call them powers to distinguish from the existing MOMENTS keyword of Multicolvars.

Examples

The following input tells plumed to calculate the coordination numbers of atoms 1-100 with themselves. The minimum coordination number is then calculated.

Click on the labels of the actions for more information on what each action computes COORDINATIONNUMBER SPECIESthis keyword is used for colvars such as coordination number. =1-100 R_0 could not find this keyword =1.0 MINcalculate the minimum value. ={BETA=0.1}


The following input tells plumed to calculate how many atoms from 1-100 are within 3.0 of each of the atoms from 101-110. In the first 101 is the central atom, in the second 102 is the central atom and so on. The number of coordination numbers more than 6 is then computed.

Click on the labels of the actions for more information on what each action computes COORDINATIONNUMBER SPECIESAthis keyword is used for colvars such as the coordination number. =101-110 SPECIESBthis keyword is used for colvars such as the coordination number. =1-100 R_0 could not find this keyword =3.0 MORE_THANcalculate the number of variables more than a certain target value. ={RATIONAL R_0=6.0 NN=6 MM=12 D_0=0}


The following input tells plumed to calculate the mean coordination number of all atoms with themselves and its powers. An explicit cutoff is set for each of 8.

Click on the labels of the actions for more information on what each action computes cn0: COORDINATIONNUMBER SPECIESthis keyword is used for colvars such as coordination number. =1-10 SWITCHThis keyword is used if you want to employ an alternative to the continuous switching
function defined above. ={RATIONAL R_0=1.0 D_MAX=8}  MEANtake the mean of these variables.
cn1: COORDINATIONNUMBER SPECIESthis keyword is used for colvars such as coordination number. =1-10 SWITCHThis keyword is used if you want to employ an alternative to the continuous switching
function defined above. ={RATIONAL R_0=1.0 D_MAX=8}  R_POWERMultiply the coordination number function by a power of r, as done in White and Voth
(see note above, default: no) =1 MEANtake the mean of these variables.
cn2: COORDINATIONNUMBER SPECIESthis keyword is used for colvars such as coordination number. =1-10 SWITCHThis keyword is used if you want to employ an alternative to the continuous switching
function defined above. ={RATIONAL R_0=1.0 D_MAX=8}  R_POWERMultiply the coordination number function by a power of r, as done in White and Voth
(see note above, default: no) =2 MEANtake the mean of these variables.
PRINT ARGthe input for this action is the scalar output from one or more other actions. =cn0.mean,cn1.mean,cn2.mean STRIDEcompulsory keyword ( default=1 )
the frequency with which the quantities of interest should be output =1 FILEthe name of the file on which to output these quantities =cn_out

Glossary of keywords and components
Description of components

When the label of this action is used as the input for a second you are not referring to a scalar quantity as you are in regular collective variables. The label is used to reference the full set of quantities calculated by the action. This is usual when using MultiColvar functions. Generally when doing this the previously calculated multicolvar will be referenced using the DATA keyword rather than ARG.

This Action can be used to calculate the following scalar quantities directly. These quantities are calculated by employing the keywords listed below. These quantities can then be referenced elsewhere in the input file by using this Action's label followed by a dot and the name of the quantity. Some of them can be calculated multiple times with different parameters. In this case the quantities calculated can be referenced elsewhere in the input by using the name of the quantity followed by a numerical identifier e.g. label.lessthan-1, label.lessthan-2 etc. When doing this and, for clarity we have made it so that the user can set a particular label for each of the components. As such by using the LABEL keyword in the description of the keyword input you can customize the component name

 Quantity Keyword Description altmin ALT_MIN the minimum value. This is calculated using the formula described in the description of the keyword so as to make it continuous. between BETWEEN the number/fraction of values within a certain range. This is calculated using one of the formula described in the description of the keyword so as to make it continuous. You can calculate this quantity multiple times using different parameters. highest HIGHEST the highest of the quantities calculated by this action lessthan LESS_THAN the number of values less than a target value. This is calculated using one of the formula described in the description of the keyword so as to make it continuous. You can calculate this quantity multiple times using different parameters. lowest LOWEST the lowest of the quantities calculated by this action max MAX the maximum value. This is calculated using the formula described in the description of the keyword so as to make it continuous. mean MEAN the mean value. The output component can be referred to elsewhere in the input file by using the label.mean min MIN the minimum value. This is calculated using the formula described in the description of the keyword so as to make it continuous. moment MOMENTS the central moments of the distribution of values. The second moment would be referenced elsewhere in the input file using label.moment-2, the third as label.moment-3, etc. morethan MORE_THAN the number of values more than a target value. This is calculated using one of the formula described in the description of the keyword so as to make it continuous. You can calculate this quantity multiple times using different parameters.
The atoms involved can be specified using
 SPECIES this keyword is used for colvars such as coordination number. In that context it specifies that plumed should calculate one coordination number for each of the atoms specified. Each of these coordination numbers specifies how many of the other specified atoms are within a certain cutoff of the central atom. You can specify the atoms here as another multicolvar action or using a MultiColvarFilter or ActionVolume action. When you do so the quantity is calculated for those atoms specified in the previous multicolvar. This is useful if you would like to calculate the Steinhardt parameter for those atoms that have a coordination number more than four for example
Or alternatively by using
 SPECIESA this keyword is used for colvars such as the coordination number. In that context it species that plumed should calculate one coordination number for each of the atoms specified in SPECIESA. Each of these coordination numbers specifies how many of the atoms specifies using SPECIESB is within the specified cutoff. As with the species keyword the input can also be specified using the label of another multicolvar SPECIESB this keyword is used for colvars such as the coordination number. It must appear with SPECIESA. For a full explanation see the documentation for that keyword
Compulsory keywords
 NN ( default=6 ) The n parameter of the switching function MM ( default=0 ) The m parameter of the switching function; 0 implies 2*NN D_0 ( default=0.0 ) The d_0 parameter of the switching function R_0 The r_0 parameter of the switching function
Options
 NUMERICAL_DERIVATIVES ( default=off ) calculate the derivatives for these quantities numerically NOPBC ( default=off ) ignore the periodic boundary conditions when calculating distances SERIAL ( default=off ) do the calculation in serial. Do not use MPI LOWMEM ( default=off ) lower the memory requirements TIMINGS ( default=off ) output information on the timings of the various parts of the calculation R_POWER Multiply the coordination number function by a power of r, as done in White and Voth (see note above, default: no) SWITCH This keyword is used if you want to employ an alternative to the continuous switching function defined above. The following provides information on the switchingfunction that are available. When this keyword is present you no longer need the NN, MM, D_0 and R_0 keywords. MEAN take the mean of these variables. The final value can be referenced using label.mean. You can use multiple instances of this keyword i.e. MEAN1, MEAN2, MEAN3... The corresponding values are then referenced using label.mean-1, label.mean-2, label.mean-3... MORE_THAN calculate the number of variables more than a certain target value. This quantity is calculated using $$\sum_i 1.0 - \sigma(s_i)$$, where $$\sigma(s)$$ is a switchingfunction. The final value can be referenced using label.morethan. You can use multiple instances of this keyword i.e. MORE_THAN1, MORE_THAN2, MORE_THAN3... The corresponding values are then referenced using label.morethan-1, label.morethan-2, label.morethan-3... LESS_THAN calculate the number of variables less than a certain target value. This quantity is calculated using $$\sum_i \sigma(s_i)$$, where $$\sigma(s)$$ is a switchingfunction. The final value can be referenced using label.lessthan. You can use multiple instances of this keyword i.e. LESS_THAN1, LESS_THAN2, LESS_THAN3... The corresponding values are then referenced using label.lessthan-1, label.lessthan-2, label.lessthan-3... MAX calculate the maximum value. To make this quantity continuous the maximum is calculated using $$\textrm{max} = \beta \log \sum_i \exp\left( \frac{s_i}{\beta}\right)$$ The value of $$\beta$$ in this function is specified using (BETA= $$\beta$$) The final value can be referenced using label.max. You can use multiple instances of this keyword i.e. MAX1, MAX2, MAX3... The corresponding values are then referenced using label.max-1, label.max-2, label.max-3... MIN calculate the minimum value. To make this quantity continuous the minimum is calculated using $$\textrm{min} = \frac{\beta}{ \log \sum_i \exp\left( \frac{\beta}{s_i} \right) }$$ The value of $$\beta$$ in this function is specified using (BETA= $$\beta$$) The final value can be referenced using label.min. You can use multiple instances of this keyword i.e. MIN1, MIN2, MIN3... The corresponding values are then referenced using label.min-1, label.min-2, label.min-3... BETWEEN calculate the number of values that are within a certain range. These quantities are calculated using kernel density estimation as described on histogrambead. The final value can be referenced using label.between. You can use multiple instances of this keyword i.e. BETWEEN1, BETWEEN2, BETWEEN3... The corresponding values are then referenced using label.between-1, label.between-2, label.between-3... HISTOGRAM calculate how many of the values fall in each of the bins of a histogram. This shortcut allows you to calculates NBIN quantities like BETWEEN. The final value can be referenced using label.histogram. You can use multiple instances of this keyword i.e. HISTOGRAM1, HISTOGRAM2, HISTOGRAM3... The corresponding values are then referenced using label.histogram-1, label.histogram-2, label.histogram-3... MOMENTS calculate the moments of the distribution of collective variables. The mth moment of a distribution is calculated using $$\frac{1}{N} \sum_{i=1}^N ( s_i - \overline{s} )^m$$, where $$\overline{s}$$ is the average for the distribution. The moments keyword takes a lists of integers as input or a range. Each integer is a value of $$m$$. The final calculated values can be referenced using moment- $$m$$. You can use the COMPONENT keyword in this action but the syntax is slightly different. If you would like the second and third moments of the third component you would use MOMENTS={COMPONENT=3 MOMENTS=2-3}. The moments would then be referred to using the labels moment-3-2 and moment-3-3. This syntax is also required if you are using numbered MOMENT keywords i.e. MOMENTS1, MOMENTS2... ALT_MIN calculate the minimum value. To make this quantity continuous the minimum is calculated using $$\textrm{min} = -\frac{1}{\beta} \log \sum_i \exp\left( -\beta s_i \right)$$ The value of $$\beta$$ in this function is specified using (BETA= $$\beta$$). The final value can be referenced using label.altmin. You can use multiple instances of this keyword i.e. ALT_MIN1, ALT_MIN2, ALT_MIN3... The corresponding values are then referenced using label.altmin-1, label.altmin-2, label.altmin-3... LOWEST this flag allows you to recover the lowest of these variables. The final value can be referenced using label.lowest HIGHEST this flag allows you to recover the highest of these variables. The final value can be referenced using label.highest